Modular Birkhoff–James orthogonality in B(X, Y) and K(X, Y)

Debmalya Sain; Ryotaro Tanaka

doi:10.1007/s43037-020-00064-z

Modular Birkhoff–James orthogonality in B(X, Y) and K(X, Y)

Debmalya Sain, Ryotaro Tanaka

Liberal Arts

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We introduce and study modular Birkhoff–James orthogonality for typical Banach modules B(X, Y) and K(X, Y) , where X and Y are Banach spaces. We present some basic characterizations of modular Birkhoff–James orthogonality under certain restrictions, and completely characterize left symmetric points for the said orthogonality relation in B(X, Y) and K(X, Y). The complications involved in an analogous study of right symmetric points are illustrated through concrete examples.

Original language	English
Pages (from-to)	1347-1362
Number of pages	16
Journal	Banach Journal of Mathematical Analysis
Volume	14
Issue number	4
DOIs	https://doi.org/10.1007/s43037-020-00064-z
Publication status	Published - 1 Sep 2020

Keywords

(Modular) Birkhoff–James orthogonality
Bounded linear operator
Compact operator
Symmetric point

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abstract = "We introduce and study modular Birkhoff–James orthogonality for typical Banach modules B(X, Y) and K(X, Y) , where X and Y are Banach spaces. We present some basic characterizations of modular Birkhoff–James orthogonality under certain restrictions, and completely characterize left symmetric points for the said orthogonality relation in B(X, Y) and K(X, Y). The complications involved in an analogous study of right symmetric points are illustrated through concrete examples.",

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AU - Tanaka, Ryotaro

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AB - We introduce and study modular Birkhoff–James orthogonality for typical Banach modules B(X, Y) and K(X, Y) , where X and Y are Banach spaces. We present some basic characterizations of modular Birkhoff–James orthogonality under certain restrictions, and completely characterize left symmetric points for the said orthogonality relation in B(X, Y) and K(X, Y). The complications involved in an analogous study of right symmetric points are illustrated through concrete examples.

KW - (Modular) Birkhoff–James orthogonality

KW - Bounded linear operator

KW - Compact operator

KW - Symmetric point

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